Problem: Simplify the following expression and state the condition under which the simplification is valid: $x = \dfrac{a^2 + 3a}{a^2 + a - 6}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{a^2 + 3a}{a^2 + a - 6} = \dfrac{(a)(a + 3)}{(a - 2)(a + 3)} $ Notice that the term $(a + 3)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(a + 3)$ gives: $x = \dfrac{a}{a - 2}$ Since we divided by $(a + 3)$, $a \neq -3$. $x = \dfrac{a}{a - 2}; \space a \neq -3$